Finite Element Model of Euler-Bernoulli Beam Theory

In summary, the Euler-Bernoulli Beam Theory formulation uses two degrees of freedom (w and dw/dx) and a cubic polynomial for interpolation. The finite element model in Chapter 5 of [1] uses a two noded element, which is subparametric due to the use of low-order elements for geometry approximation. The requester is looking for a reference for an FE model using isoparametric elements. The ANSYS FEA package has robust documentation on its beam and link elements, which may be helpful.
  • #1
Ali Baig
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In the formulation of Euler-Bernoulli Beam Theory, there are two degrees of freedom at a point, w and dw/dx. Typically, the finite element model of this theory uses cubic polynomial for interpolation of $w$ using a two noded element as given in Chapter 5 of this book [1]. This element is a subparametric because the geometry is represented by low-order elements than those used to approximate the dependent variable. I need a reference where I can find the FE model for this problem using isoparametric elements. [1]: https://www.amazon.com/dp/0072466855/?tag=pfamazon01-20
 
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  • #2
Have you researched any of the beam element formulations for specific FEA packages? Ansys's element documentation is fairly robust for example, you can read more about them here: Sharcnet.ca: ANSYS Beam and Link Elements
 

1. What is a Finite Element Model (FEM) of Euler-Bernoulli Beam Theory?

A Finite Element Model is a numerical method used to analyze complex structural systems, such as beams, by dividing them into smaller, simpler elements. The Euler-Bernoulli Beam Theory is a mathematical model that describes the behavior of beams under load, taking into account factors such as bending and deflection.

2. How is a FEM of Euler-Bernoulli Beam Theory created?

A FEM of Euler-Bernoulli Beam Theory is created by dividing the beam into smaller elements, such as triangles or rectangles, and assigning mathematical equations to each element based on the properties of the material and the applied load. These equations are then solved simultaneously to determine the behavior of the entire beam.

3. What are the advantages of using a FEM of Euler-Bernoulli Beam Theory?

One of the main advantages of using a FEM of Euler-Bernoulli Beam Theory is its ability to model complex structural systems with high accuracy. It also allows for easy visualization of the beam's behavior and can provide insights into areas of high stress or potential failure. Additionally, FEM can be used to optimize designs and reduce material and manufacturing costs.

4. What are the limitations of a FEM of Euler-Bernoulli Beam Theory?

While FEM of Euler-Bernoulli Beam Theory is a powerful tool, it also has some limitations. It is a numerical method and therefore relies on assumptions and simplifications, which may not accurately capture the real-world behavior of the beam. Additionally, FEM requires significant computational power and time to solve complex problems.

5. How is a FEM of Euler-Bernoulli Beam Theory validated?

A FEM of Euler-Bernoulli Beam Theory can be validated by comparing its results to experimental data or analytical solutions. This helps ensure that the assumptions and simplifications made in the model are appropriate and that the results are accurate. Additionally, sensitivity analyses can be performed to determine the effects of changing input parameters on the results.

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